Well, if the i3 is bad, then what choice do you have?
Honestly, the i7 will be a great upgrade. However, it might be more cost effective to put an SSD into that Dell as I doubt it has one. The i3 should be more than sufficient for what you are doing, but the hard drive might be holding you back. Your computer is only as fast as the data it is being fed in most applications. Going from a 5400 rpm mechanical drive to ANY SSD will be absolutely night and day. I had an i5 6200U laptop that came with a mechanical drive. It was ok, but I was used to my desktop that had an SSD. One day I just got sick of how slow that laptop was and bought a 480 GB Sandisk SSD. Windows installed quickly, and from the first boot that laptop was transformed. I kept it for 2 years after that and never again felt that it was slow.
Even that i7, if it doesn't have an SSD, will feel slow.